Density versions of Schur's theorem for ideals generated by submeasures

Journal of Combinatorial Theory. Series A

Volumn 117, Issue 7, 2010, Pages 943-956

  Filipów, Rafał ^a   Szuca, Piotr ^a  

^a UNIVERSITY OF GDA SK   (Poland)

Author keywords

Bolzano Weierstrass property; Bolzano Weierstrass theorem; Ideal convergence; Schur's theorem; Statistical convergence; Statistical density; Subsequence

Indexed keywords

EID: 77953811728     PISSN: 00973165     EISSN: 10960899     Source Type: Journal    
DOI: 10.1016/j.jcta.2009.12.005     Document Type: Article

References (14)

1. Bergelson Vitaly A density statement generalizing Schur's theorem. J. Combin. Theory Ser. A 1986, 43(2):338-343.
2. Bergelson Vitaly, Hindman Neil Density versions of two generalizations of Schur's theorem. J. Combin. Theory Ser. A 1988, 48(1):32-38.
3. Blanchard Peter F., Harary Frank, Reis Rogério Partitions into sum-free sets. Integers 2006, 6. A7, 10 pp. (electronic).
4. Farah Ilijas Analytic quotients: theory of liftings for quotients over analytic ideals on the integers. Mem. Amer. Math. Soc. 2000, 148(702). xvi+177.
5. Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca, Ideal version of Ramsey's theorem, submitted for publication.
6. Filipów Rafał, Mrożek Nikodem, Recław Ireneusz, Szuca Piotr Ideal convergence of bounded sequences. J. Symbolic Logic 2007, 72(2):501-512.
7. Frankl P., Graham R.L., Rödl V. Iterated combinatorial density theorems. J. Combin. Theory Ser. A 1990, 54(1):95-111.
8. Just Winfried, Krawczyk Adam On certain Boolean algebras P(ω)/I. Trans. Amer. Math. Soc. 1984, 285(1):411-429.
9. Kojman Menachem van der Waerden spaces. Proc. Amer. Math. Soc. 2002, 130(3):631-635. (electronic).
10. Louveau Alain, Veličković Boban A note on Borel equivalence relations. Proc. Amer. Math. Soc. 1994, 120(1):255-259.
11. Mazur Krzysztof Fσ-ideals and ω1ω1*-gaps in the Boolean algebras P(ω)/I. Fund. Math. 1991, 138(2):103-111.
12. Solecki Sławomir Analytic ideals and their applications. Ann. Pure Appl. Logic 1999, 99(1-3):51-72.
13. Todorcevic Stevo Topics in Topology. Lecture Notes in Math. 1997, vol. 1652. Springer-Verlag, Berlin.
14. Visser Cornelis On Poincaré's recurrence theorem. Bull. Amer. Math. Soc. 1936, 42(6):397-400.